CN116238058B - Efficient low-loss processing method for brittle material - Google Patents

Abstract

The invention discloses a high-efficiency and low-loss processing method for brittle materials, which belongs to the technical field of precision processing of brittle materials. It includes the following steps: 1) After determining the brittle material to be processed, determine the critical cutting depth of unidirectional crack propagation for the brittle material to be processed; 2) Determine the actual processing depth of the brittle material to be processed, the actual processing depth is less than The critical depth of cut for unidirectional crack propagation in brittle materials; 3) Perform tool setting on the pre-machined surface of the workpiece, adjust the tool posture, make the tool rotate a certain angle to the feed direction of the pre-feed tool, and cooperate with the tool to adjust the machining along the vibration track The brittle material is cut; using multiple passes, the cracks on the machined surface produced by this pass that are biased toward the feed direction of the pre-feed will be removed in the next pass, and the cycle goes back and forth to achieve brittle materials. processing. Through the method, the cutting depth of low-damage machining of brittle materials can be effectively improved, and the cutting efficiency is high and the cost is low.

Description

A high-efficiency and low-loss processing method for brittle materials

technical field

The invention discloses a high-efficiency and low-loss processing method for brittle materials, which belongs to the technical field of precision processing of brittle materials.

Background technique

With the development of ultra-precision processing technology, brittle materials (such as single crystal silicon, ceramics, glass and other hard and brittle materials and cadmium zinc telluride, calcium fluoride, zinc selenide and other soft and brittle materials) are used in aerospace, national defense, microelectronics, etc. Information and optical manufacturing and other fields have been widely used. However, brittle materials have low fracture toughness and are prone to cracks during processing, resulting in extremely poor machinability. The processing efficiency and precision are affected by defects such as microcracks, which limits the development of its further application. Therefore, how to achieve high-efficiency and low-damage precision machining of brittle materials is the key to promoting its further application and the rapid development of related fields, and it is also a key issue that needs to be solved in the industry. In response to this problem, many scholars have carried out research on related methods and equipment, and achieved many beneficial results. At present, the high-quality processing of brittle materials still relies on grinding and polishing technology, and its processing efficiency is low. In order to improve the machinability of brittle materials, some scholars have proposed methods such as laser-assisted processing, surface modification, and vibration-assisted processing, in an attempt to further improve processing efficiency while ensuring processing quality. The effectiveness of the above methods has also been experimentally confirmed. verify. However, laser-assisted processing is limited by the complexity and high cost of equipment, and surface modification will introduce other ions on the surface of the matrix material to cause surface contamination. Compared with laser-assisted machining and surface modification, vibration-assisted machining is an effective means to achieve high-efficiency, low-cost, and low-damage creation of brittle materials, but its corresponding critical depth of cut for brittle-plastic transition is usually lower. At present, the basic idea of improving the processing efficiency of brittle materials is to control the actual cutting depth within the critical cutting depth of brittle-plastic transition by increasing the critical cutting depth of brittle-plastic transition, so as to realize the ductile removal of brittle materials. Laser-assisted machining, surface modification, and vibration-assisted machining are all aimed at improving the critical cutting depth of brittle-plastic transition of brittle materials, which to some extent limits the development of methods and technologies for improving the machinability of brittle materials. Therefore, the current low-cost, high-efficiency, and ductile precision machining technology for brittle materials needs to be further developed, so as to meet the wider application requirements in various related fields.

Chinese patent CN114226866A discloses a method of cyclic vibration cutting with set trajectory, which discloses the following technical content: when the actual cutting thickness is greater than the critical cutting thickness, if the brittle crack generated by cutting in the brittle zone has not propagated to the ideal processing surface depth, the instantaneous crack can be Cutting off directly by the next vibration cycle without affecting the quality of the final machined surface. However, the critical cutting thickness it said is actually the critical cutting depth of the brittle-plastic transition, and it has not found that there is a critical cutting depth for unidirectional crack propagation, so it cannot control the direction of crack propagation, which causes the tool to move in the direction of lateral feed. Cracks in the opposite direction cannot be eliminated. If two directions are processed, the processing efficiency will be reduced. On this basis, the cutting depth is limited, and the efficiency cannot be greatly improved.

Contents of the invention

The technical problem to be solved by the present invention is: to overcome the deficiencies of the prior art, to provide a high-efficiency and low-loss processing method for brittle materials, which can actively control the propagation direction of micro-cracks in the processing process, and realize the critical cutting depth of brittle materials in the brittle-plastic transition Low-damage plastic processing outside the limit has the advantages of high efficiency and low cost.

The technical solution adopted by the present invention to solve the technical problem is: the high-efficiency and low-loss processing method for brittle materials, which is characterized in that it includes the following steps:

1) After determining the brittle material to be processed, determine the critical depth of cut for unidirectional crack propagation for the brittle material to be processed;

The critical depth of cut for unidirectional crack growth is the depth of cut when the crack on the surface of the groove is only on one side of the groove and the crack is about to extend to the bottom of the groove when the tool is machining brittle materials. Side deflection, so that the cutting edge of the tool forms an included angle with the cutting speed direction;

2) Determine the actual processing depth of the brittle material to be processed. The actual processing depth is greater than the critical cutting depth of the brittle-plastic transition and less than the critical cutting depth of the unidirectional crack propagation. The critical cutting depth of the brittle-plastic transition is the first place in the groove. Depth of cut for crack damage, the actual depth of cut is less than the critical depth of cut for unidirectional crack propagation, that is, the depth of cut before reaching the critical depth of cut for unidirectional crack propagation, so that the cracks on the processed surface distributed on one side under the actual depth of cut are farther away from the groove There is a certain distance from the bottom;

3) Carry out tool setting on the pre-processed surface of the workpiece, and adjust the tool posture to deflect the tool at a certain angle to the lateral feed direction, the cutting edge of the tool forms an included angle with the cutting speed direction, and cooperate with the tool to move along the planned vibration trajectory. The brittle material to be processed is cut; using multiple tool passes, the cracks on the machined surface that are biased toward the feed direction of the pre-feed produced by this pass will be removed during the next pass, and the cycle is repeated to achieve Processing of brittle materials.

Further, the method for determining the critical depth of cut for unidirectional crack propagation in step 1) is as follows:

The tool performs continuous scoring with variable cutting depth on the brittle material to be processed until the crack in the scored groove extends to at least the bottom of the groove.

Further, the brittle material to be processed is fixed at a certain angle to the horizontal plane, and the tool continuously marks the brittle material to be processed at the fixed inclination, so that the cutting depth increases along the cutting direction.

Further, the deflection angle of the tool in step 3) is the same as the deflection angle of the tool in step 1).

Further, in step 3), the attitude of the tool is adjusted by the precision rotating platform, and the precision rotating platform rotates the tool without changing the position of the tool tip to realize the change of the tool attitude. The precision rotary platform is installed on the processing machine tool, the tool is fixed on the precision rotary platform, and the attitude of the tool is precisely adjusted.

Further, in step 2), the infeed amount of the tool is also determined. The determination of the infeed amount of the tool is to partially overlap the tool contours of the continuous cutting tool, so as to ensure that the next cutting tool will eliminate the residual machining surface cracks in this cutting tool. Chip removal.

According to the vibration trajectory of the tool in the selected tool modulation cutting mode, the attitude of the tool is adjusted, so that the tool can be rotated at a certain angle to achieve bevel cutting, and the bevel cutting and the vibration track of the tool can cooperate with each other, so that the cracks on the workpiece processing surface can be in a certain range. Depth expands to one side.

Further, in step 3), the tool cuts the brittle material to be processed by means of an elliptical vibration trajectory.

Further, the elliptical vibration track is a two-dimensional elliptical vibration or a three-dimensional elliptical vibration.

Compared with prior art, the beneficial effect that the present invention has is:

The present invention firstly determines the critical cutting depth of the unidirectional crack propagation of the brittle material to be processed, and the actual processing depth is greater than the critical cutting depth of the brittle-plastic transition, so that the cracks generated during the processing are only biased to one side of the feed direction of the cutting tool, and will be processed in the next time. It is removed during the cutting process and reciprocated to realize efficient ductile and low-damage processing of brittle materials outside the critical cutting depth limit of brittle-plastic transition. Through this method, the cutting depth of brittle materials and low-damage processing can be effectively improved, with high cutting efficiency and low cost. Low.

When the cutting edge of the tool is perpendicular to the direction of cutting speed, the cracks generated in the cutting groove expand to both sides, and when the cutting edge of the tool is deflected by a certain angle, that is, the cutting edge of the tool is not perpendicular to the direction of cutting speed, The cracks in the cutting groove will be concentrated on one side of the groove, and the cracks are located on one side of the cutting direction, and there are no cracks in the groove in the opposite direction, so that the critical depth of cut for unidirectional crack propagation can be found and the depth of cut can be improved. At the same time, the remaining machining surface cracks left by this cutting pass are removed by the next cutting pass.

Also by determining the lateral feed rate of the tool, it is ensured that the next tool pass will remove the machining surface cracks left by this tool pass, leaving only the machined surface with low surface damage, and further improving the processing efficiency while ensuring the processing quality .

Description of drawings

Figure 1 is a three-dimensional schematic diagram of the high-efficiency and low-loss processing method for brittle materials.

Fig. 2 is a top view of the principle schematic diagram of the high-efficiency and low-loss processing method for brittle materials.

Fig. 3 is a schematic diagram of continuous scribing with variable depth of cut to determine the critical depth of cut for unidirectional crack propagation.

Fig. 4 is an image of a single crystal silicon groove under an optical microscope scribed by a three-dimensional elliptical vibration-assisted oblique cutting method with a variable cutting depth.

Fig. 5 is a schematic diagram of the principle of planar high-efficiency and low-damage machining of flat workpieces.

Fig. 6 is a schematic diagram of the principle of high-efficiency and low-damage machining of the end face of a cylindrical workpiece.

Fig. 7 is a schematic diagram of the principle of high-efficiency and low-damage machining of cylindrical workpieces.

Among them: 1. Tool 2. Brittle material 3. Critical depth of cut for brittle-plastic transition 4. Critical depth of cut for unidirectional crack propagation 5. Cracks;

In the figure, θ is the angle between the orientation of the tool face and the cutting speed direction, a is the cutting direction, b is the tool vibration trajectory, C is the C axis of the machine tool, L1 is the position of the critical depth of cut for unidirectional crack propagation, and L2 is the brittle The position of the critical cutting depth of plastic transformation, S is the crack damage area, c1 is the first cutting tool cutting, c2 is the second cutting cutting, c3 is the third cutting cutting, c4 is the fourth cutting cutting .

Detailed ways

Figures 1 to 7 are the best embodiments of the high-efficiency and low-loss processing method for brittle materials, and the present invention will be further described below in conjunction with accompanying drawings 1 to 7.

Referring to Figures 1-2, the high-efficiency and low-loss processing method for brittle materials specifically includes the following steps:

1) Determine the surface shape to be processed, select the brittle material 2 and tool 1 to be processed; the surface shape to be processed can be selected as plane, cylindrical surface and cylindrical end surface, and the brittle material 2 to be processed can be selected from single crystal silicon, ceramics, For hard and brittle materials or soft and brittle materials such as optical glass, sapphire, and KDP crystal, the cutting tool 1 generally adopts a diamond tool.

2) Fix the workpiece to be processed on the movement axis of the ultra-precision machine tool according to the surface shape to be processed, and select the appropriate configuration form of the tool 1; use the four-axis x , y , z , and c-axis ultra-precision machine tool to perform different surface processing in the preferred embodiment According to the shape of the machined surface, which is plane, cylindrical surface and cylindrical end surface, respectively fix the workpiece at a suitable position on the C-axis, adjust the attitude of the tool 1 so that the rake face faces the feed direction of the tool and forms an angle θ with the direction of the cutting speed, Then the movement of the tool 1 in the directions of x- axis, y -axis and z -axis can be controlled to perform tool setting and realize the processing principle shown in Fig. 1 and Fig. 2 .

3) Select the modulation cutting mode of tool 1.

4) Adjust the attitude of the tool 1 to rotate the tool 1 at a certain angle so that the cutting edge of the tool 1 is not perpendicular to the direction of the cutting speed.

5) Adjust the processing parameters, and determine the critical depth of cut 3 for the brittle-plastic transition and the critical depth of cut 4 for unidirectional crack growth for the brittle material 2 to be processed.

6) According to the dimensional characteristics of the processing target and the critical depth of cut for unidirectional crack growth 4, determine the actual machining depth of cut, determine the lateral feed of each tool pass, and plan the movement path of the tool 1 in combination with the specifications of the selected tool 1 , optimize the process parameters and form NC codes, and import the codes into the ultra-precision machine tool control system.

7) Perform tool setting on the pre-processed surface of the workpiece and start processing.

8) Carry out high-efficiency and low-damage processing of brittle material 2 based on the above steps based on ultra-precision machine tools. Through the adjustment of tool 1 attitude and the coordination of tool 1 vibration trajectory, multiple tool passes are used to achieve high-efficiency and low-damage processing of brittle material 2 .

In the above step 8), the attitude of the tool 1 is adjusted by the precision rotating platform, and the precision rotating platform rotates the tool 1 without changing the position of the tool tip to realize the change of the attitude of the tool 1. The precision rotary platform is installed on the processing machine tool, the tool 1 is fixed on the precision rotary platform, and the attitude of the tool 1 is precisely adjusted. The tool 1 cuts the brittle material 2 to be processed by means of a vibration trajectory. The vibration trajectory includes but is not limited to two-dimensional elliptical vibration and three-dimensional elliptical vibration. The appropriate tool 1 modulation cutting method is selected according to the shape of the surface to be processed.

After testing, it can be found that when the tool 1 deflects so that the cutting edge of the tool 1 is not perpendicular to the cutting speed direction, and the cutting depth is within a certain range, the crack 5 generated by the tool 1 processing the workpiece only expands to the side where the tool 1 is deflected, while the cutting depth is within a certain range. It will not expand to the other side, the depth range is the critical depth of cut for brittle-plastic transition 3 to the critical depth of cut for unidirectional crack growth 4, and the critical depth of cut for brittle-plastic transition 3 and the critical depth of cut for unidirectional crack growth for each material 4 are all different and need to be tested for each material.

See Figures 3~4, the above step 5) The method for determining the critical depth of cut 4 for unidirectional crack growth is as follows:

The cutting tool 1 is rotated at a certain angle to the feed direction of the pre-feed, and the brittle material 2 to be processed is continuously marked with variable depth of cut. The bottom side is about to reach the depth of the bottom of the groove, and the critical depth of cut 3 for the brittle-plastic transition is the cutting depth at which the first crack damage occurs when the brittle material 2 is cut.

In this embodiment, the monocrystalline silicon workpiece is the brittle material 2 as an example, and the machining method of adjusting the attitude of the tool 1 and assisting cutting with three-dimensional elliptical vibration is used to process grooves of the typical brittle material 2 monocrystalline silicon plane with variable cutting depth, as shown in Fig. 3 The middle arrow a is the cutting direction, and the arrow b is the vibration trajectory of tool 1. By applying a three-dimensional elliptical vibration displacement signal to tool 1, locking the C axis, tilting the monocrystalline silicon workpiece by 0.1°, increasing the cutting depth along the cutting direction, and adjusting tool 1 The inclination angle is 30°, and the groove surface morphology shown in Figure 4 is obtained by performing variable cutting depth machining. The dotted line L2 in Figure 4 is the critical depth of cut 3 for the brittle-plastic transition. The position of the crack damage, when the cutting depth is less than the critical cutting depth 3 of the brittle-plastic transition of single crystal silicon, no crack 5 damage occurs on the surface of the groove, and when the cutting depth is greater than the brittle-plastic transition critical cutting depth 3 of single crystal silicon, the groove Crack 5 damage occurs on the surface of the groove, but the crack 5 damage occurs only on one side of the groove, and there is no crack 5 damage at the bottom of the groove. The dotted line L1 in Figure 4 is the position of the critical depth of cut 4 for unidirectional crack propagation. At this time, the crack damage is about to extend to the bottom of the groove. It can be seen from Fig. 4 that the crack damage in area S is biased towards the side of the machined surface, indicating that within the critical depth of cut 4 for unidirectional crack propagation, the processing parameters can be set to Fixed, using multiple passes, the next pass can remove the crack 5 damage caused by this pass, and the cycle goes back and forth to process a smooth surface with high efficiency, low cost and low damage. The inclination angle of the tool 1 is not limited to 30°, and other angles can also be selected.

The brittle material 2 is processed by adjusting the attitude of the tool 1 and assisting the cutting with two-dimensional or three-dimensional elliptical vibration. By applying a two-dimensional or three-dimensional elliptical vibration displacement signal to the tool 1, it is convenient to move the tool 1 along the x-axis. Forming the motion track of tool 1 as shown in Figure 1, machining at a depth within the critical depth of cut 4 for unidirectional crack propagation will cause crack damage concentrated on one side of the workpiece surface, as shown in Figure 2, and the other side is Smooth surface, using multiple passes, the cracks 5 on the machined surface produced by this pass that are biased towards the feed direction of the pre-feed will be removed in the next pass, and the cycle is repeated, which is efficient and low-cost , Process the surface of smooth and brittle materials with low damage.

See Figure 5. In the figure, c1 is the first tool pass, c2 is the second tool pass, and c3 is the third tool pass. The processing method of adjusting the tool 1 attitude and assisting cutting with two-dimensional or three-dimensional elliptical vibration is used to process flat plates. The plane of the brittle material 2 is processed. By applying a two-dimensional or three-dimensional elliptical vibration displacement signal to the tool 1 and cooperating with the movement of the tool 1 along the x direction, the brittle material 2 can be cut at the critical point of the brittle-plastic transition through multiple tool passes. High-efficiency and low-damage machining beyond the limit of depth 3, cutting the plane of the flat workpiece, so that the tool 1 deflects toward the unprocessed surface of the workpiece, because the real-time cutting depth is greater than the critical cutting depth 3 of the brittle-plastic transition under the corresponding parameters, so in the second Cracks 5 damage remained on the side close to the unprocessed surface during the first pass. At this time, these brittle cracks did not extend to the bottom of the groove processed by this pass. Therefore, by controlling the lateral feed, in the third pass During the cutting process, the crack 5 damage caused by the last cutting pass can be completely removed. In Figure 5, the crack 5 damage left by the first cross-feed cutting has been removed by the second cutting pass, leaving only smooth processed Surface, reciprocating cycle, just obtain the efficient, low-cost, ductile processing of planar brittle material 2 workpieces.

See Figure 6. In the figure, c1 is the first tool pass, c2 is the second tool pass, and c3 is the third tool pass. The processing method of adjusting the tool 1 attitude and assisting cutting with two-dimensional or three-dimensional elliptical vibration is used for cylindrical The end face of the brittle material 2 is processed. By applying a two-dimensional or three-dimensional elliptical vibration displacement signal to the tool 1 and cooperating with the rotational movement of the C axis, the brittle material 2 can be cut outside the ductile cutting depth limit by sequentially feeding the tool. High-efficiency ductile machining, as shown in Figure 6, cuts the end face of a cylindrical workpiece, deflects the tool 1 toward the unprocessed side of the workpiece, controls the cutting depth within the critical cutting depth 4 of the unidirectional crack propagation, and makes the processed surface crack 5 Expanding to one side, the other side is a smooth surface. At this time, these brittle cracks have not touched the bottom of the groove processed by this pass. Therefore, by controlling the feed rate, during the third pass The crack 5 damage caused by the second cutting tool can be completely removed, and the reciprocating cycle can obtain the high-efficiency, low-cost, and low-damage processing of the brittle material 2 workpiece on the cylindrical end surface.

See Figure 7, c1 in the figure is the first tool pass, c2 is the second tool pass, c3 is the third tool pass, c4 is the fourth tool pass, and the attitude of tool 1 is adjusted to cooperate with two-dimensional or three-dimensional elliptical vibration The processing method of the trajectory processes the outer surface of the cylindrical brittle material 2. By applying a two-dimensional or three-dimensional elliptical vibration displacement signal to the tool 1 and coordinating with the rotational movement of the C axis, the brittleness can be achieved by sequentially feeding the tool. High-efficiency ductile machining of material 2 outside the ductile depth of cut limit, as shown in Figure 7, cutting the outer circular surface of a cylindrical workpiece, so that the tool 1 is deflected toward the unprocessed side of the workpiece, and the cutting depth is controlled between the critical depth of cut for brittle-plastic transition 3 and Machining between the critical depth of cut 4 for unidirectional crack propagation makes the processed surface crack 5 propagate toward one side of the feed direction of the pre-feed, and the other side is a smooth surface. The bottom of the groove processed by the tool pass, so by controlling the feed rate of the tool pass, the crack 5 damage caused by the third pass can be completely removed in the fourth pass, and the cylindrical outer circle can be obtained by reciprocating cycles. High-efficiency, low-cost, and low-damage machining of workpieces with brittle surfaces.

When the cutting edge of the tool 1 is perpendicular to the direction of the cutting speed, the crack 5 generated in the cutting groove expands to both sides, and when the cutting edge of the tool 1 is deflected by a certain angle, that is, the cutting edge of the tool 1 and the cutting speed If the direction is not vertical, the cracks 5 in the cutting groove will be concentrated on one side of the groove, and the cracks 5 are located on one side of the cutting direction, and there are no cracks in the groove in the opposite direction, so that the material can be found by testing. The critical depth of cut for unidirectional crack propagation is 4. While increasing the depth of cut, the residual cracks on the machined surface of this cutting pass are removed through the next cutting pass, thereby effectively improving the processing efficiency.

The above is only a preferred embodiment of the present invention, and is not intended to limit the present invention to other forms. Any skilled person who is familiar with this profession may use the technical content disclosed above to change or modify the equivalent of equivalent changes. Example. However, any simple modifications, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solution of the present invention still belong to the protection scope of the technical solution of the present invention.

Claims (8)

1. A high-efficiency and low-loss processing method for brittle materials, characterized in that: comprising the following steps: 1) After determining the brittle material (2) to be processed, determine the critical depth of cut (4) for unidirectional crack propagation for the brittle material (2) to be processed; The critical depth of cut for unidirectional crack growth (4) is the process of tool (1) machining brittle materials (2), the crack (5) generated on the surface of the groove is only on one side of the groove, and the crack (5) is about to extend to the groove Cutting depth at the bottommost position of the groove, the tool (1) deflects to one side during machining, so that the cutting edge of the tool (1) forms an included angle with the cutting speed direction; 2) Determine the actual processing depth of the brittle material (2) to be processed, and the actual processing depth is less than the critical depth of cut for unidirectional crack propagation (4); 3) Perform tool setting on the pre-processed surface of the workpiece, and adjust the attitude of the tool (1) so that the tool (1) deflects a certain angle in the direction of lateral feed, and the cutting edge of the tool (1) forms an included angle with the cutting speed direction, And cooperate with the tool (1) to cut the brittle material (2) to be processed along the planned vibration trajectory; using multiple tool passes, the cracks (5) generated by this tool pass will be removed in the next tool pass , reciprocating, to realize the processing of brittle materials (2). 2. The high-efficiency and low-damage processing method for brittle materials according to claim 1, characterized in that: in step 1), the method for determining the critical depth of cut (4) for unidirectional crack propagation is as follows: The tool (1) continuously marks the brittle material (2) to be processed with variable cutting depth until the crack (5) in the scored groove extends to at least the bottom of the groove. 3. The high-efficiency and low-loss processing method for brittle materials according to claim 2, characterized in that: the brittle material (2) to be processed is fixed at a certain angle to the horizontal plane, and the tool (1) is fixed against the brittle material (2) to be processed Continuous scoring is performed so that the depth of cut increases in the cutting direction. 4. The high-efficiency and low-loss machining method for brittle materials according to claim 1, characterized in that: the deflection angle of the tool (1) in step 3) is the same as the deflection angle of the tool (1) in step 1). 5. The high-efficiency and low-loss processing method for brittle materials according to claim 1, characterized in that: in step 3), the posture of the tool (1) is adjusted by the precision rotating platform, and the precision rotating platform rotates without changing the position of the tool tip The tool (1) realizes the attitude change of the tool (1). 6. The high-efficiency and low-loss processing method for brittle materials according to claim 1, characterized in that: in step 2), the infeed of the tool (1) is also determined, and the infeed of the tool (1) is determined by making The tool contours of the continuous cutting tool overlap partially to ensure that the next cutting tool cutting will remove the machining surface cracks (5) remaining in this cutting tool cutting. 7. The high-efficiency and low-loss processing method for brittle materials according to claim 1, characterized in that: in step 3), the tool (1) cuts the brittle material (2) to be processed by adopting an elliptical vibration trajectory. 8. The high-efficiency and low-loss processing method for brittle materials according to claim 7, wherein the elliptical vibration track is a two-dimensional elliptical vibration or a three-dimensional elliptical vibration.

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